Non-public networks (NPN) - Private Networks by another name

3GPP TS 22.261, Service requirements for the 5G system; Stage 1 gives a definition of non-public network which is simply defined as 'a network that is intended for non-public use'. Section 6.25 provides more info

Non-public networks are intended for the sole use of a private entity such as an enterprise, and may be deployed in a variety of configurations, utilising both virtual and physical elements. Specifically, they may be deployed as completely standalone networks, they may be hosted by a PLMN, or they may be offered as a slice of a PLMN.

In any of these deployment options, it is expected that unauthorised UEs, those that are not associated with the enterprise, will not attempt to access the non-public network, which could result in resources being used to reject that UE and thereby not be available for the UEs of the enterprise. It is also expected that UEs of the enterprise will not attempt to access a network they are not authorised to access. For example, some enterprise UEs may be restricted to only access the non-public network of the enterprise, even if PLMN coverage is available in the same geographic area. Other enterprise UEs may be able to access both a non-public network and a PLMN where specifically allowed.

The requirements section is interesting too:

• The 5G system shall support non-public networks.
• The 5G system shall support non-public networks that provide coverage within a specific geographic area.
• The 5G system shall support both physical and virtual non-public networks. 
• The 5G system shall support standalone operation of a non-public network, i.e. a non-public network may be able to operate without dependency on a PLMN.
• Subject to an agreement between the operators and service providers, operator policies and the regional or national regulatory requirements, the 5G system shall support for non-public network subscribers:
• access to subscribed PLMN services via the non-public network;
• seamless service continuity for subscribed PLMN services between a non-public network and a PLMN;
• access to selected non-public network services via a PLMN;
• seamless service continuity for non-public network services between a non-public network and a PLMN.
• A non-public network subscriber to access a PLMN service shall have a service subscription using 3GPP identifiers and credentials provided or accepted by a PLMN.
• The 5G system shall support a mechanism for a UE to identify and select a non-public network.
• NOTE: Different network selection mechanisms may be used for physical vs virtual non-public networks.
• The 5G system shall support identifiers for a large number of non-public networks to minimize collision likelihood between assigned identifiers.
• The 5G system shall support a mechanism to prevent a UE with a subscription to a non-public network from automatically selecting and attaching to a PLMN or non-public network it is not authorised to select.
• The 5G system shall support a mechanism to prevent a UE with a subscription to a PLMN from automatically selecting and attaching to a non-public network it is not authorised to select. 
• The 5G system shall support a change of host of a non-public network from one PLMN to another PLMN without changing the network selection information stored in the UEs of the non-public network.

I think it's like M2M (Machine-to-Machine) that is used commonly by the industry but the term used in 3GPP standards are MTC (Machine Type Communications)

— Zahid Ghadialy (@zahidtg) May 6, 2019

5G ACIA (5G Alliance for Connected Industries and Automation), a Working Party of ZVEI (German Electrical and Electronic Manufacturers’ Association) published a White Paper on '5G Non-Public Networks for Industrial Scenarios'.

This paper describes four industrial (IIoT) deployment scenarios for 3GPP-defined 5G non-public networks. The paper also considers key aspects, in particular service attributes that can help to highlight the differences between these scenarios. In contrast to a network that offers mobile network services to the general public, a 5G non-public network (NPN, also sometimes called a private network) provides 5G network services to a clearly defined user organisation or group of organisations.

The PDF of the white paper is available here.